Question

r = 8sin(Theta). Write an equation in rectangular coordinates.

Answer 1

what are x and y in polar?!?!

Answer 2

"Transform the polar equation to an equation in rectangular coordinates" is all it says ...

Answer 3

but everyone is telling me to use this formula:
x = rcosθ
y = rsinθ
x² + y² = r²

Answer 4

yes

that's right

so \(r = 8 \sin( \theta)\) is the same as

\(\sqrt{x^2 + y^2} = 8\dfrac{ y}{\sqrt{x^2 + y^2}}\)

Answer 5

Yes but I am not sure how to solve this..

Answer 6

multiply each side by \(\sqrt{x^2 + y^2}\)

Answer 7

\[\sqrt{x^2 + y^2} * \sqrt{x^2 + y^2} = 8\dfrac{ y}{\sqrt{x^2 + y^2}}*\sqrt{x^2 + y^2} \]

Answer 8

??

Answer 9

\[\sqrt{x^2 + y^2} * \sqrt{x^2 + y^2} = x^2 + y^2 \]

right?!

Answer 10

and

\[\dfrac{ y}{\sqrt{x^2 + y^2}}*\sqrt{x^2 + y^2} = y\]

yes?